The Russian third seed, who beat the Swiss for the first time in the semi-finals of the ATP World Tour Finals in November, repeated the feat to progress to Saturday's final where he will face world number two Rafael Nadal.
"I'd beaten him once, so I knew I could beat him again. Then I thought, why not this time? I concentrated more on baseline and serves," Davydenko, who has lost 12 times to Federer, told a news conference.
"In the second set, it was getting tougher as both of us were tired and couldn't run fast. It was a difficult situation but fortune favored me. I think my serve has improved lately."
Federer committed 37 unforced errors and had no answer to many of the world number six's powerful cross-court shots.
"He deserved the lead, held it and finished the game. Hats off to him. It isn't that I played too badly, but he played better," said Federer.
"I like to come to Doha every year. I'm excited to go to Australia too and I need some rest before the year's first Slam (this month's Australian Open)."
Unlike Federer, Spain's Nadal stuck to the script and defeated Serbian fifth seed Viktor Troicki 6-1 6-3.
"I had the match under my control right from the beginning. After the first two games, my confidence grew, and my serve and volley were better.
"Since there were more people around to witness the action, I had more motivation. An easy victory against Viktor has boosted my confidence."
Davydenko said he would try to stay focused in the final.
"Both Rafa and I are basically baseline players. He's going to play much stronger and harder, so I'll have to focus more on my game," said the Russian.
"It will all depend on how long I can hold him."
(Editing by Sonia Oxley)